Sum of terms of an AP:

An arithmetic progression (AP) is a sequence of numbers in which the difference of any two successive members is constant. The sum of the terms of an AP can be calculated using the formula S_n = n/2 [2a + (n-1)d], where S_n is the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.

Given sum of terms:

In this case, the sum of the terms of the AP is given as 3n^2 + 5n.

Deriving the AP:

By comparing the given sum with the formula for the sum of terms of an AP, we can equate the two expressions:
3n^2 + 5n = n/2 [2a + (n-1)d]

Solving this equation will give us the values of a and d, which are the first term and common difference of the AP.

Series of the AP:

Once we have determined the values of a and d, we can generate the series of the AP by starting with the first term a and successively adding the common difference d to each term.

Conclusion:

In conclusion, the given sum of terms of an AP can be used to derive the first term and common difference of the AP, which can then be used to generate the series of the AP. This process involves using the formula for the sum of terms of an AP and solving the resulting equation to find the required values.